BRUSSELS — After more than a year of hard bargaining, European finance ministers on Wednesday reached a political agreement on a final piece of the bloc's planned banking union, which is the most ambitious step in integrating Europe's economy since the adoption of the common currency.

The ministers said they agreed on the guidelines for a new joint European institution in charge of closing down or propping up ailing banks, the so-called single resolution mechanism, complete with an arrangement to finance its operations.